List of edo-distinct 58et rank two temperaments

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This revision was by author genewardsmith and made on 2014-06-17 21:30:07 UTC.
The original revision id was 514265532.
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Original Wikitext content:

The temperaments listed are 58edo-distinct, meaning that they are all different even if tuned in 58edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

=5-limit temperaments= 
|| Period generator || Wedgie || Name || Complexity || Commas ||
|| 58 19 || <<14 1 -31]] || || 7.0510 || 6442450944/6103515625 ||
|| 29 10 || <<30 -2 -73]] || || 15.837 || 9444732965739290427392/8381903171539306640625 ||
|| 58 1 || <<16 -3 -42]] || || 8.828 || 4398046511104/4119873046875 ||
|| 29 9 || <<2 -4 -11]] || || 2.121 || 2048/2025 ||
|| 58 21 || <<12 5 -20]] || || 5.522 || 254803968/244140625 ||
|| 29 1 || <<26 6 -51]] || || 12.488 || 1641562064176545792/1490116119384765625 ||
|| 58 17 || <<18 -7 -53]] || || 10.731 || 9007199254740992/8342742919921875 ||
|| 29 11 || <<54 8 -113]] || || 26.555 || [113 8 -54> ||
|| 58 3 || <<10 9 -9]] || || 4.502 || 10077696/9765625 ||
|| 29 8 || <<34 48 -3]] || || 17.206 || 638131544614980078906888/582076609134674072265625 ||
|| 58 23 || <<20 -11 -64]] || || 12.703 || 18446744073709551616/16894054412841796875 ||
|| 29 2 || <<6 46 59]] || || 14.875 || 9007199254740992000000/8862938119652501095929 ||
|| 58 15 || <<8 13 2]] || || 4.363 || 1594323/1562500 ||
|| 29 12 || <<22 14 -29]] || || 9.851 || 2567836929097728/2384185791015625 ||
|| 58 5 || <<22 43 17]] || || 13.625 || 328256967394537077627/312500 ||
|| 29 7 || <<50 16 -91]] || || 23.481 || [91 16 -50> ||
|| 58 25 || <<6 17 13]] || || 5.177 || 129140163/128000000 ||
|| 29 3 || <<38 40 -25]] || || 17.490 || 407943558924674501581996032/363797880709171295166015625 ||
|| 58 13 || <<34 19 -49]] || || 15.323 || 654295038711035754184704/582076609134674072265625 ||
|| 29 13 || <<10 38 37]] || || 11.672 || 1350851717672992089/1342177280000000000 ||
|| 58 7 || <<4 21 24]] || || 6.600 || 10485760000/10460353203 ||
|| 29 6 || <<18 22 -7]] || || 8.609 || 4016775629952/3814697265625 ||
|| 58 27 || <<26 35 -5]] || || 12.886 || 1601009443167990624/1490116119384765625 ||
|| 29 4 || <<46 24 -69]] || || 20.822 || [69 24 -46> ||
|| 58 11 || <<2 25 35]] || || 8.326 || 858993459200/847288609443 ||
|| 29 14 || <<42 32 -47]] || || 18.755 || 260789407250723664179754958848/227373675443232059478759765625 ||
|| 58 9 || <<28 31 -16]] || || 13.029 || 40479843698864750592/37252902984619140625 ||
|| 29 5 || <<14 30 15]] || || 9.338 || 205891132094649/200000000000000 ||
|| 2 1 || <<0 29 46]] || || 10.202 || 70368744177664/68630377364883 ||

Original HTML content:

<html><head><title>List of edo-distinct 58et rank two temperaments</title></head><body>The temperaments listed are 58edo-distinct, meaning that they are all different even if tuned in 58edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5-limit temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->5-limit temperaments</h1>
 

<table class="wiki_table">
    <tr>
        <td>Period generator<br />
</td>
        <td>Wedgie<br />
</td>
        <td>Name<br />
</td>
        <td>Complexity<br />
</td>
        <td>Commas<br />
</td>
    </tr>
    <tr>
        <td>58 19<br />
</td>
        <td>&lt;&lt;14 1 -31]]<br />
</td>
        <td><br />
</td>
        <td>7.0510<br />
</td>
        <td>6442450944/6103515625<br />
</td>
    </tr>
    <tr>
        <td>29 10<br />
</td>
        <td>&lt;&lt;30 -2 -73]]<br />
</td>
        <td><br />
</td>
        <td>15.837<br />
</td>
        <td>9444732965739290427392/8381903171539306640625<br />
</td>
    </tr>
    <tr>
        <td>58 1<br />
</td>
        <td>&lt;&lt;16 -3 -42]]<br />
</td>
        <td><br />
</td>
        <td>8.828<br />
</td>
        <td>4398046511104/4119873046875<br />
</td>
    </tr>
    <tr>
        <td>29 9<br />
</td>
        <td>&lt;&lt;2 -4 -11]]<br />
</td>
        <td><br />
</td>
        <td>2.121<br />
</td>
        <td>2048/2025<br />
</td>
    </tr>
    <tr>
        <td>58 21<br />
</td>
        <td>&lt;&lt;12 5 -20]]<br />
</td>
        <td><br />
</td>
        <td>5.522<br />
</td>
        <td>254803968/244140625<br />
</td>
    </tr>
    <tr>
        <td>29 1<br />
</td>
        <td>&lt;&lt;26 6 -51]]<br />
</td>
        <td><br />
</td>
        <td>12.488<br />
</td>
        <td>1641562064176545792/1490116119384765625<br />
</td>
    </tr>
    <tr>
        <td>58 17<br />
</td>
        <td>&lt;&lt;18 -7 -53]]<br />
</td>
        <td><br />
</td>
        <td>10.731<br />
</td>
        <td>9007199254740992/8342742919921875<br />
</td>
    </tr>
    <tr>
        <td>29 11<br />
</td>
        <td>&lt;&lt;54 8 -113]]<br />
</td>
        <td><br />
</td>
        <td>26.555<br />
</td>
        <td>[113 8 -54&gt;<br />
</td>
    </tr>
    <tr>
        <td>58 3<br />
</td>
        <td>&lt;&lt;10 9 -9]]<br />
</td>
        <td><br />
</td>
        <td>4.502<br />
</td>
        <td>10077696/9765625<br />
</td>
    </tr>
    <tr>
        <td>29 8<br />
</td>
        <td>&lt;&lt;34 48 -3]]<br />
</td>
        <td><br />
</td>
        <td>17.206<br />
</td>
        <td>638131544614980078906888/582076609134674072265625<br />
</td>
    </tr>
    <tr>
        <td>58 23<br />
</td>
        <td>&lt;&lt;20 -11 -64]]<br />
</td>
        <td><br />
</td>
        <td>12.703<br />
</td>
        <td>18446744073709551616/16894054412841796875<br />
</td>
    </tr>
    <tr>
        <td>29 2<br />
</td>
        <td>&lt;&lt;6 46 59]]<br />
</td>
        <td><br />
</td>
        <td>14.875<br />
</td>
        <td>9007199254740992000000/8862938119652501095929<br />
</td>
    </tr>
    <tr>
        <td>58 15<br />
</td>
        <td>&lt;&lt;8 13 2]]<br />
</td>
        <td><br />
</td>
        <td>4.363<br />
</td>
        <td>1594323/1562500<br />
</td>
    </tr>
    <tr>
        <td>29 12<br />
</td>
        <td>&lt;&lt;22 14 -29]]<br />
</td>
        <td><br />
</td>
        <td>9.851<br />
</td>
        <td>2567836929097728/2384185791015625<br />
</td>
    </tr>
    <tr>
        <td>58 5<br />
</td>
        <td>&lt;&lt;22 43 17]]<br />
</td>
        <td><br />
</td>
        <td>13.625<br />
</td>
        <td>328256967394537077627/312500<br />
</td>
    </tr>
    <tr>
        <td>29 7<br />
</td>
        <td>&lt;&lt;50 16 -91]]<br />
</td>
        <td><br />
</td>
        <td>23.481<br />
</td>
        <td>[91 16 -50&gt;<br />
</td>
    </tr>
    <tr>
        <td>58 25<br />
</td>
        <td>&lt;&lt;6 17 13]]<br />
</td>
        <td><br />
</td>
        <td>5.177<br />
</td>
        <td>129140163/128000000<br />
</td>
    </tr>
    <tr>
        <td>29 3<br />
</td>
        <td>&lt;&lt;38 40 -25]]<br />
</td>
        <td><br />
</td>
        <td>17.490<br />
</td>
        <td>407943558924674501581996032/363797880709171295166015625<br />
</td>
    </tr>
    <tr>
        <td>58 13<br />
</td>
        <td>&lt;&lt;34 19 -49]]<br />
</td>
        <td><br />
</td>
        <td>15.323<br />
</td>
        <td>654295038711035754184704/582076609134674072265625<br />
</td>
    </tr>
    <tr>
        <td>29 13<br />
</td>
        <td>&lt;&lt;10 38 37]]<br />
</td>
        <td><br />
</td>
        <td>11.672<br />
</td>
        <td>1350851717672992089/1342177280000000000<br />
</td>
    </tr>
    <tr>
        <td>58 7<br />
</td>
        <td>&lt;&lt;4 21 24]]<br />
</td>
        <td><br />
</td>
        <td>6.600<br />
</td>
        <td>10485760000/10460353203<br />
</td>
    </tr>
    <tr>
        <td>29 6<br />
</td>
        <td>&lt;&lt;18 22 -7]]<br />
</td>
        <td><br />
</td>
        <td>8.609<br />
</td>
        <td>4016775629952/3814697265625<br />
</td>
    </tr>
    <tr>
        <td>58 27<br />
</td>
        <td>&lt;&lt;26 35 -5]]<br />
</td>
        <td><br />
</td>
        <td>12.886<br />
</td>
        <td>1601009443167990624/1490116119384765625<br />
</td>
    </tr>
    <tr>
        <td>29 4<br />
</td>
        <td>&lt;&lt;46 24 -69]]<br />
</td>
        <td><br />
</td>
        <td>20.822<br />
</td>
        <td>[69 24 -46&gt;<br />
</td>
    </tr>
    <tr>
        <td>58 11<br />
</td>
        <td>&lt;&lt;2 25 35]]<br />
</td>
        <td><br />
</td>
        <td>8.326<br />
</td>
        <td>858993459200/847288609443<br />
</td>
    </tr>
    <tr>
        <td>29 14<br />
</td>
        <td>&lt;&lt;42 32 -47]]<br />
</td>
        <td><br />
</td>
        <td>18.755<br />
</td>
        <td>260789407250723664179754958848/227373675443232059478759765625<br />
</td>
    </tr>
    <tr>
        <td>58 9<br />
</td>
        <td>&lt;&lt;28 31 -16]]<br />
</td>
        <td><br />
</td>
        <td>13.029<br />
</td>
        <td>40479843698864750592/37252902984619140625<br />
</td>
    </tr>
    <tr>
        <td>29 5<br />
</td>
        <td>&lt;&lt;14 30 15]]<br />
</td>
        <td><br />
</td>
        <td>9.338<br />
</td>
        <td>205891132094649/200000000000000<br />
</td>
    </tr>
    <tr>
        <td>2 1<br />
</td>
        <td>&lt;&lt;0 29 46]]<br />
</td>
        <td><br />
</td>
        <td>10.202<br />
</td>
        <td>70368744177664/68630377364883<br />
</td>
    </tr>
</table>

</body></html>
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